FIG. 1 is a flow diagram of a sound recording flow of a conventional sound recording system 100, also referred to as a microphone system, according to an embodiment. The sound recording system 100 may include two main modules: a transducer 110 (located in a microphone) and an analog-to-digital converter (ADC) 150. The transducer 110 contains a diaphragm 120. The diaphragm 120 vibrates due to sound pressure, producing a proportional change in voltage. The ADC 150 measures this voltage variation (at a fixed sampling frequency) and stores the resultant digital samples in memory. The digital samples represent the recorded sound in the digital domain.
To function in practice, the sound recording system 100 may further include a pre-amplifier 130 and a low-pass filter (LPF) 140 situated in the signal path between the diaphragm 120 and the ADC 150. The pre-amplifier 130 may amplify the output of the transducer 110 by a gain of around ten times so that the ADC 150 can measure the signal effectively using its predefined quantization levels. Without this amplification, the signal may be too weak (around tens of millivolts). The LPF 140 may eliminate high-frequency or other extraneous noise.
As per Nyquist's law, if the ADC's sampling frequency is fs Hz, the sound is band-limited to (fs/2) Hz to avoid aliasing and distortions. Since natural sound can spread over a wide band of frequencies, the sound may be low pass filtered (e.g., frequencies greater than f(fs/2) Hz are removed) before the analog-to-digital conversion. As ADCs in today's microphones operate at 48 kHz, the low pass filters are designed to cut off signals at 24 kHz.
FIG. 2 is a block diagram illustrating creation of the digital spectrum by the sound recording system 100 of FIG. 1, with and without the anti-aliasing low-pass filter 140, according to an embodiment. Note the aliasing noise present in the spectrum output of the case without the LPF 140 and the absence of that aliasing noise in the case with the LPR.
Sound playback is simply the reverse of recording. Given a digital signal as input, a digital-to-analog converter (DAC) produces the corresponding analog signal and feeds it to a speaker. The speaker's diaphragm oscillates to the applied voltage producing varying sound pressures in the medium, which is then audible to humans.
Modules inside a microphone are mostly linear systems, meaning that the output signals are linear combinations of the input. In the case of the pre-amplifier 130, if the input sound is S, then the output may be represented by Sout=A1S. Here, A1 is a complex gain that can change the phase and/or amplitude of the input frequencies, but does not generate spurious new frequencies. This behavior makes it possible to record an exact (but higher-power) replica of the input sound and playback without distortion.